Exercise 1.In the
episode “Homer Defined” (8F04) of The Simpsons, Homer reads a copy of
the "US of A Today" newspaper.

Homer: Here's good news!According to this eye-catching article, SAT scores are
declining at a slower rate!

Lisa:Dad, I think this paper
is a flimsy hodgepodge of pie graphs, factoids and Larry King.

Homer:Hey, this is the only
paper in America that's not afraid to tell the truth, that everything is
just fine.

Describe and sketch the shape of the graph of SAT
scores over time, using Homer’s description.You should mention derivatives in your explanation.

Exercise 2.The slogan
of the Lowe’s Home Improvement company is
“Improving Home Improvement.”

Assuming that this is what the company really does, explain
how there is a second derivative at work in this slogan.

First,

define or explain what is meant by home
improvement.

Next, identify a relevant function and variable (obviously
you will not give a formula), and then analyze what the first two derivatives
(and their signs) mean.

Possible hints:First,
try to find a first derivative of a function in the slogan.A complete correct response to this exercise could consist of just a few sentences.

Exercise 3.The following quote by mathematician Hugo Rossi appeared in the article,
“Mathematics is an Edifice, Not a Toolbox” in Notices of the American
Mathematical Society, Vol. 43, No. 10, Oct. 1996:

"In the fall
of 1972 President Nixon announced that the rate of increase of inflation was
decreasing. This was the first time a sitting president used the third
derivative to advance his case for reelection."

Explain
Rossi’s analysis of Nixon’s statement, by identifying a relevant function
and variable (a formula is not required), and explaining Nixon’s use of a
third derivative.

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